Note that \(A\)  is a (1,1)-tensor (or a field of operators, which is more obvious than in [1]},
when written in proper indices), so condition () means that \(A\)  is symmetric with respect to
metric \(\phi \) : \(\phi (A\xi ,\eta )=\phi (\xi ,A\eta )\) .
However \(A\)  is a given field and the unknown in this equation is \(\phi \) . Yet, there are many solutions
(depending on arbitrary functions).
